# Math Help - Linear optimization

1. ## Linear optimization

A pension fund manager decides to invest a total of at most $39 million in U.S. treasury bonds paying 4% annual interest and in mutual funds paying 8% annual interest. He plans to invest at least$5 million in
bonds and at least $10 million in mutual funds. Bonds have an initial fee of$100 per million dollars,
while the fee for mutual funds is $200 per million. The fund manager is allowed to spend no more than$5000 on fees. How much should be invested in each to maximize annual interest? What is the maximum
annual interest?

How would i set up the max and min and then eventually graph it? and thus solve the problem
Thank you

2. ## Re: Trignomy word problem

Hello, Niaboc!

I'll set it up . . .

A pension fund manager decides to invest a total of at most $39 million in Treasury Bonds paying 4% annual interest and in Mutual Funds paying 8% annual interest. He plans to invest at least$5 million in Trasury Bonds and at least $10 million in Mutual Funds. Treasury Bonds have an initial fee of$100 per million dollars, while the fee for Mutual Funds is $200 per million. The fund manager is allowed to spend no more than$5000 on fees.

How much should be invested in each to maximize annual interest?
What is the maximum annual interest?

Let $x$ = amount invested in Treasury Bonds (in millions of dollars): $x\ge\,0$
Let $y$ = amount invested in Mutual Funds (in millions of dollars): . $y \,\ge\,0$

Total invested, $39 million: . $x + y \:\le\:39$ Invest at least$10 million in Mutual Funds: . $x \,\ge\,10$
Invest at least $5 million in Treasure Bonds: . $y \,\ge\,5$ Fee for Treasury Bonds: $100x$ Fee for Mutual Funds: $200y$ Maximum fee,$5000: . $100x + 200y \,\le\,5000$

Maximize interest: . $I \:=\:0.04x + 0.08y$